GTA Vice City was made for the PlayStation 2. The PS2 has a 300MHz CPU with 32MB RAM, and a GPU with 6.2 GFLOPS (slightly simplifying, it wasn't a standard PC architecture). The game was read from DVD, and the DVD drive could push 5.28 MB/s (if everything was sequential on the disk).
So it's safe to assume that the difference is mostly due to advances in tech, though advances in compression algorithms likely also helped (not that the PS2 had a lot of spare CPU cycles to decompress content).
I tried it with Vice City, it took a bit longer to load for me. That said, it looks a lot smaller than I remember it being.